NONLINEAR DYNAMIC BEHAVIORS OF A THERMO-MECHANICAL COUPLING VISCOELASTIC PLATE

摘要

In the article, the nonlinear dynamic model of a thermo-mechanical coupling viscoelastic rectangular plate with the varied temperature field and subjected to both actions of an alternating periodic transverse external excitation and in-plane uniform distributed force is established. The model, which is considered the influence of heat conduction, thermal expansion and viscosity, is obtained by means of the constitutive description of thermo-viscoelastic material obey the Boltzman’s superposition principle and the dynamic equilibrium equation of the rectangular plate on the basis of the Karman theory for thin plates with large deflection and the thermo-viscoelastic energy theory. It may be converted to a nonlinear differential-integral dynamical system by using Galerkin’s method. Based on the nonlinear integral-ordinary differential dynamical system of the thermomechanical coupling viscoelastic plate, the general nonlinear numerical method for viscoelastic plate is obtained by introducing difference method. And then, a kind of special dynamic model with thermo-mechanical coupling is solved. Finally, synthetically using several methods in dynamic systems, the dynamic properties of the thermo-mechanical coupling viscoelastic plate are sufficiently revealed. It is found that the dynamic properties of the thermo-mechanical coupling viscoelastic plate subjected to both actions of an alternating periodic transverse external excitation and in-plane uniform distributed force are abundant, and the chaos is greater than the viscoelastic plate’s without the influence of temperature, especially, the motion state of hyperchaos appears.